So far I've resisted posting in this thread, but no more.
I don't think anyone has mentioned how weight is distributed on the sidestand vs. the centerstand. On the sidestand, the majority of the weight is still on the wheels, and only the leaning of the motorcycle is supported by the stand. The use of a pad of some sort on asphalt is a no brainer. On the centerstand, the entire weight of the motorcycle is balanced on the stand right in the middle of the motorcycle. The wheels aren't a factor.
I foolishly put my motorcycle (only once) on its centerstand on asphalt. The tipover was rather catastrophic. Never again. Sidestand, in gear, at all parking facilities. At home, in the garage, on a nice smooth cement floor where no one's going to bump it, it's not going to sink in the asphalt, and could easily be worked on...that's where my bikes are on their centerstands.
At the gas station, centerstand for the reasons mentioned above; easier to have a level service for any gear that needs to be removed, and also allows a complete fill.
When it comes to taking any of my motorcycles off either the centerstand or the sidestand, I'm always astride the bike. That's what works for me.
Not telling anyone what to do, everyone will do what works for them. I'm just sayin' what works for me.